NANO LETTERS
Direct Observation of the Mechanical Properties of Single-Walled Carbon Nanotubes and Their Junctions at the Atomic Level
2003 Vol. 3, No. 6 751-755
H. E. Troiani,† M. Miki-Yoshida,†,‡ G. A. Camacho-Bragado,† M. A. L. Marques,§ A. Rubio,§ J. A. Ascencio,| and M. Jose-Yacaman*,†,⊥ Texas Materials Institute and Department of Chemical Engineering, UniVersity of Texas at Austin, 78712 Austin, Texas, Centro de InVestigacio´ n en Materiales AVanzados, Miguel de CerVantes 120, Chihuahua, Chih., CP 31109, Me´ xico, Dpto. de Fı´sica de Materiales, Facultad de Quı´mica, UniVersidad del Paı´s Vasco, Centro Mixto CSIC/UPV, and Donostia International Physics Center, Paseo Manuel Lardiza´ bal 4, 20018 San Sebastia´ n, Spain, Programa Ductos, Instituto Mexicano del Petro´ leo, Me´ xico DF, Me´ xico, and Instituto de Fı´sica, UNAM, Me´ xico DF, Me´ xico Received March 18, 2003; Revised Manuscript Received April 9, 2003
ABSTRACT Starting from an amorphous C film, single-walled carbon nanotubes were obtained in situ in a high-resolution electron microscope by the combined effect of irradiation and axial strain. Ductile nanotubes developed either a junction or a linear chain of C atoms before failure. These facts have been put in direct evidence for the first time. Tight-binding calculations indicate that the bonding in the linear chain is of a cumulene type.
Since the discovery of carbon nanotubes (CNTs),1 they have become one of the most intensively studied materials.2-23 Their mechanical and electronic properties make them one of the most promising building blocks of future high-strength materials and nanodevices.2,3 Due to the strength of the carbon-carbon bond, one of the strongest in nature, CNTs may exhibit an extremely high Young’s modulus on the order of 1 TPa,4 which clearly indicates the extraordinary axial stiffness of these materials. It is therefore not surprising that a large experimental5-10 and theoretical11-15 effort has been devoted to the study of the elastic properties of single-walled carbon nanotubes (SWCNTs). Most of the experimental work has been established on indirect transmission electron microscopy (TEM) observation of post-mortem specimens or in situ buckling of nanotubes.5,6,16 Treacy et al.6 determined the Young’s modulus of SWCNTs by measuring their free-standing vibration amplitude. Other researchers used in situ resonant excitation of multiwalled carbon nanotubes * Corresponding author. E-mail:
[email protected]. † University of Texas at Austin. ‡ Centro de Investigacio ´ n en Materiales Avanzados. § Universidad del Paı´s Vasco and Donostia International Physics Center. | Instituto Mexicano del Petro ´ leo. ⊥ Instituto de Fı´sica, UNAM. 10.1021/nl0341640 CCC: $25.00 Published on Web 04/25/2003
© 2003 American Chemical Society
(MWCNTs) in a TEM.17 Recently, Demczyk et al. carried out direct measurements of the tensile force at failure and Young’s modulus of MWCNTs using a tensile testing microstage inside a TEM.18 In addition to TEM-based methods, atomic force microscopy and related techniques have been also used to measure the mechanical properties of CNTs.7,9,10,19 A proposed mechanism for the release of stress in strained SWCNTs is the formation of Stone-Wales defects20 which act as a nucleus of relaxation for both the plastic deformation and brittle cleavage of nanotubes.14,21-23 In the present work we have produced SWCNTs using the intense beam of a field emission TEM that we further irradiated to induce an axial strain on the tube. The technique for the generation of the nanotubes was a similar to the one used by Kondo and Takayanagi24 to make Au nanowires. We were able to fabricate SWCNTs down to a diameter of 0.33 nm in a reproducible way. The experiments were performed in a high-resolution transmission electron microscope (HRTEM) equipped with a field emission electron gun of 200 kV (JEM-2010F), which additionally allowed the examination of the failure mechanisms of SWCNTs at high resolution.
Figure 2. High-resolution transmission electron microscopy images of the failure of brittle and ductile SWCNT. (a) Brittle SWCNT just before its fracture. (b) and (c) After breaking the brittle SWCNT remains vibrating anchored to the graphite. (d) Image of a ductile SWCNT spanning between two nanofibers. (e) The tube starts to develop a neck. (f) Formation of two quasi-fullerene cages in contact with each other.
Figure 1. (a) Initial stage of the carbon fiber formed by intense electron irradiation at 200 keV. (b) Vibrating state of the fiber that is produced when the outer layer breaks. (c) The carbon becomes graphitic under electron irradiation. (d) A SWCNT of 0.57 nm is formed.
The starting material was a thin film (20-30 nm thick) of amorphous carbon, on top of which we deposited metal (Au or Pd) nanoparticles. The role of the nanoparticles was to promote the carbon diffusion. The C film was first irradiated with the electron beam in order to create two neighboring holes. For this purpose, a high initial beam dose of ∼180 A/cm2 was used. Once the holes were opened, the wall between them formed a carbon fiber. At this stage the current was reduced to normal imaging values, around 2040 A/cm2. The less intense electron beam induced graphitization on the amorphous fiber. At the same time the holes enlarged, leading to a net force that stressed the carbon fiber in an analogous mode to that reported by Lourie and Wagner for SWCNT ropes bridging a hole in a polymer film.25 The initial state of the fiber is shown in Figure 1a. At this stage, we observed a strong deformation of the outermost graphitic layer, which eventually breaks.11 This process is enhanced by the creation of defects by the electron beam.26,27 It is wellknown that the formation of vacancies and defects under high-energy particle irradiation (for electrons at energies higher than 80 keV) induces structural transformations in graphitic structures.26 In some stage of the straining process a disruption of the lattice structure occurs along the axis of the nanofiber,10 inducing in a first instance its complete amorphization, as illustrated in Figure 1b. After the disruption 752
damps the nanofiber becomes graphitic again. The elongation and thinning process goes on until a thin fiber of about 5 layers (0.33 nm each) is produced (Figure 1c). Further irradiation leads to the production of a SWCNT between two graphitic cones, as shown in Figure 1d. The dimensions of the produced nanotube vary from 0.33 to 1.0 nm in diameter and 3 to 5 nm in length. SWCNT presented two failure mechanisms: brittle fracture and plastic yielding. In the former case, the fracture occurs before any plastic deformation (Figure 2a,b). After breaking, the SWCNT vibrates anchored at one end to the graphite (Figures 2b,c). All brittle SWCNTs exhibit similar mechanical properties. The ductile tubes undergo plastic deformation before fracture; an example is shown in Figures 2d and 2e. In several cases, we have observed bending of the SWCNT up to 90° with respect to the original tube axis.7 Just before breaking one can observe the formation of two fullerene cages in contact with each other (Figure 2f). The angle formed by the joint cages and the axial direction of the SWCNT is ∼120°. As mentioned above, the carbon nanotubes release spontaneously the excess strain energy by the formation of topological Stone-Wales defects. In this process, the 90° rotation of one C-C bond produces two pentagons and two heptagons that wind themselves at 120° around the axis of the tube. Our results then support the idea that the nucleation of Stone-Wales defects occurs during the strain and eventually causes the fracture. In addition, at large strain regimes, Stone-Wales defects may split, triggering the separation and gliding of 5-7 dislocations.14,21 This can lead to the production of a local change in diameter and chirality of the tube, and to the formation of a junction, such as the structure shown in Figure 2e. This junction is stable, and does not break if the irradiation is stopped. To determine the structure of the junction we performed extensive image simulations using the SimulaTEM software package.28 Calibrating the magnification using the graphite lines near the SWCNT Nano Lett., Vol. 3, No. 6, 2003
Figure 3. (a) Necking of the tube develops until a 0.33 nm SWCNT is formed. (b) The SWCNT elongated by about 50% before breaking.
Figure 4. Longitudinal coupled oscillation of a SWCNT (top), a C-chain, and a MWCNT (bottom). (a) Monatomic C-chain probably of cumulene type. (b) C-chain contracts under stress. (c) Breaking of the C-chain. The failure occurs at the contact points between the chain and the nanotube.
reduced the error in the determination of the size of the nanotubes, allowing us to correct the changes in the diameter due to defocus. One should also take into account that the images of the nanotubes have a diameter slightly different from the real value.29 To our best judgment, the nanotubes correspond to the (7,0) and (4,0) zigzag structures, since the formation of this (7,0) (4,0) (7,0) junction can be achieved by the creation and splitting of successive Stone-Wales defects.14,21 We believe that the electron beam irradiation induces the 90° local bond rotations that generate these defects. The (7,0) SWCNT is semiconducting, although a few percent of Stone-Wales defects may reduce the gap dramatically and even render the tube metallic.30 This raises the possibility of performing in situ band-gap engineering of SWCNTs using electron irradiation. At a certain point of the deformation process the tube starts necking, this is the onset of the formation of a 0.33 nm ((0.04 nm) nanotube (Figure 3a), such necking has been predicted by molecular dynamics simulations and observed in experiments on metallic nanowires.31 We believe this narrow tube corresponds to a (4,0) zigzag nanotube. Such 0.33 nm tubes were recently reported in the literature.29 However, they were found at the intersection of two SWCNT and were of very short length. The (4,0) tube is extremely elastic and can be elongated by about 50% before breaking (Figure 3b). In this case we can roughly estimate the stress resistance of the SWCNT; considering the variation of the Nano Lett., Vol. 3, No. 6, 2003
dimension of the hole before and after the fracture and assuming that it was essentially composed of graphite. The tensile strength of the SWCNT can be estimated as 100 GPa. Then considering that the nanotube undergoes only elastic deformation and taking the strain at fracture of 0.5, we obtain 200 GPa as a lower limit value for the Young’s modulus. Another interesting phenomenon that was observed is the formation of a single chain of carbon atoms (see Figure 4) spanning two nanotube fragments before fracture; to the best of our knowledge this is the first direct TEM observation of these chains. They were theoretically predicted for the high strain rate fracture of CNTs11 and experimentally identified in laser-vaporized graphite samples32,33 and in the field emission of electrons from biased carbon nanotubes.34 These chains are remarkably stable; we have observed prior to the C-chain fracture the coupled longitudinal oscillation of a SWCNT, a C-chain, and a MWCNT for around 20 s (Figure 4a,b). The tensile force onto the C-chain was estimated using the force constant k8 obtained by tight-binding calculations for a linear C-chain of 8 atoms (k8 ∼ 52 N m-1, see below). Considering the measured elongation of the chain (∆Lch ∼ 0.14 ( 0.03 nm), the tensile force applied to the chain is estimated as Fch ∼ 7.3 ( 1.6 nN. Subsequently, the tensile stress σSWCNT applied to the adjacent SWCNT was estimated taking into account its cross sectional area (diameter dSWCNT ∼ 0.67 ( 0.05 nm) and the tensile force, thus σSWCNT ∼ 21 ( 7.5 GPa. Finally, the Young’s modulus of the SWCNT 753
Figure 5. Typical geometry used in the tight-binding calculations. A chain of up to 9 atoms is placed between two cone-terminated nanotubes. Minimization of these structures leads to a cumulene-type chain (see text for details). Table 1. Results of the Tight-Binding Calculations of the Force Constant and Length of Monatomic C-Chain as a Function of the Number of Atomsa # of atoms
force constant N m-1
length nm
1 2 3 4 5 6 7 8 9
81 72 74 66 65 60 56 52 51
4.189 4.325 4.452 4.586 4.713 4.847 4.974 5.107 5.235
a In the length of the structure it is included the two finite size tubes adjacent to the chain (around 4 nm).
can be evaluated by measuring its strain ∼ 0.068 ( 0.01, then we obtain YSWCNT ∼ 305 ( 156 GPa. To understand the formation mechanism and the structural properties of the one-dimensional C-chains, extensive tightbinding calculations have been performed.35 The initial geometry consists of two finite size tubes terminated with cone-like defective structures. The two pieces are bridged by a linear chain of carbon atoms (see Figure 5). For each applied external strain the structure is relaxed. The knockon collisions of the high-energetic electrons with carbon atoms are simulated by a random removal of a few atoms in the constriction. In this way, vacancies are created that promote the transfer of carbon atoms from the cone to the chain. The energy of the electron beam (200 keV) provides enough energy to drive this process.36,37 Increasing the distance between the tube ends does not break the chain. Instead, it elongates by incorporating atoms from the contact region. During the elongation, the strain energy is not uniformly distributed over the whole structure. On average, 40% is accumulated in the elongated chain and the rest mainly in the contact region. Fracture most likely occurs at the contact between the chain and the nanotube. This is in agreement with experimental observations (Figure 4c). We have performed calculations of the internal energy, force constant and length of the structure as a function of the number of C atoms in the chain (1 to 9 atoms). Table 1 presents the results for the force constant and length of the structure. The equilibrium bond length between carbon atoms was found to lie between 0.127 and 0.134 nm; these results are in agreement with those of Bianchetti et al.38 Moreover, the bonding are probably of cumulene type (:CdC‚‚‚ CdC:), with nearly equivalent bond lengths,39 with only a 754
small “dimerization” (less than 2%). This is consistent with first-principle calculations for free-standing carbon chains.36 Chains with less than 10 atoms are predicted to be of cumulene type; however, if the number of atoms increases, the linear configuration becomes unstable. This may be the reason we did not observe chains larger than 1 nm. In conclusion, with our method we were able to generate several carbon nanostructures, ranging from junctions to small diameter nanotubes (0.33 nm), and one-dimensional chains of carbon atoms. Several unique mechanical behaviors of SWCNTs were observed at high resolution. This opens new exciting possibilities for the study of mechanical and transport properties of SWCNT and carbon atomic chains. Acknowledgment. This work was supported by the CONYCYT, Argentina, by special funds from Texas Materials Institute and the Center for Nano and Molecular Technology (UT-Austin), CONACYT, Me´xico, the University of the Basque Country, DGES, and by the EU research training network NANOPHASE (HPRN-CT-2000-00167). References (1) Iijima, S. Nature 1991, 354. (2) Carbon Nanotubes; Dresselhaus, M. S., Dresselhaus, G., Avouris, Ph., Eds.; Springer-Verlag: Berlin, 2001. (3) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787-792. and references therein. (4) Salvetat-Delmotte; J.-P.; Rubio, A. Carbon 2002, 40, 1729-1734 and references therein. (5) Chopra, N. G.; Benedict, L. X.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zettl, A. Nature 1995, 377, 135-138. (6) Treacy, M. M. J.; Ebbesen, T. W.; Gibson, J. M. Nature 1996, 381, 678-680. (7) Wong, E. W.; Sheehan, P. E.; Lieber, C. M. Science 1997, 277, 1971-1975. (8) Krishnan, A.; Dujardin, E.; Ebbesen, T. W.; Yianilos, P. N.; Treacy, M. M. J. Phys. ReV. B 1998, 58, 14013-14019. (9) Salvetat, J. P.; Bonard, J. M.; Thomson, N. H.; Kulik, A. J.; Forro, L.; Benoit, W.; Zuppiroli, L. Appl. Phys. A 1999, 69, 255-260. (10) Yu, M.-F.; Lourie, O.; Dyer, M. J.; Moloni, K.; Kelly, T. F.; Ruoff, R. S. Science 2000, 287, 637-640. (11) Yakobson, B. I.; Campbell, M. P.; Brabec, C. J.; Bernholc, J. Comput. Mater. Sci. 1997, 8, 341-348. (12) Ping Lu, J. Phys. ReV. Lett. 1997, 79, 1297-1300. (13) Herna´ndez, E.; Goze, C.; Bernier, P.; Rubio, A. Phys. ReV. Lett. 1998, 80, 4502-4505. (14) Nardelli, B. M.; Yakobson, B. I.; Bernholc, J. Phys. ReV. Lett. 1998, 81, 4656-4659. Zhao, Q.; Nardelli, M. B.; Bernholc, J. Phys. ReV. B 2002, 65, 144105-144110. (15) Orlikowski, D.; Nardelli, B.; Marco, D.; Bernholc, J.; Roland, C. Phys. ReV. Lett. 1999, 83, 4132-4135. (16) Iijima, S.; Brabec, C.; Maiti, A.; Bernholc, J. J. Chem. Phys. 1996, 104, 2089-2092. Falvo, M. R.; Clary, G. J.; Taylor, R. M., II.; Chi, V.; Brooks, F. P., Jr; Washburn, S.; Superfine, R. Nature 1997, 389, 582-584. Lourie, O.; Cox, D. M.; Wagner, H. D. Phys. ReV. Lett. 1998, 81, 1638-1641. Nano Lett., Vol. 3, No. 6, 2003
(17) Poncharal, P.; Wang, Z. L.; Ugarte, D.; De Heer, W. A. Science 1999, 283, 1513-1516. (18) Demczyk, B. G.; Wang, Y. M.; Curnings, J.; Hetman, M.; Han, W.; Zettl, A.; Ritchie, R. O. Mater. Sci. Eng. A 2002, A334, 173-178. (19) Volodin, A.; Ahlskog, M.; Seynaeve, E.; Van Haesendonck, C.; Fonseca, A.; Nagy, J. B. Phys. ReV. Lett. 2000, 84, 3342-3345. (20) Stone, A. J.; Wales, D. J. Chem. Phys. Lett. 1986, 128, 501-503. (21) Yakobson, B. I. Appl. Phys. Lett. 1998, 72, 918-920. (22) Zhang, P.; Lammert, P. E.; Crespi, V. H. Phys. ReV. Lett. 1998, 81, 5346-5349. (23) Srivastava, D.; Menon, M.; Cho, K. Phys. ReV. Lett. 1999, 83, 29732976. (24) Kondo, Y.; Takayanagi, K. Phys. ReV. Lett. 1997, 79, 3455-3458. (25) Lourie, O.; Wagner, H. D. Appl. Phys. Lett. 1998, 73, 3527-3529. (26) Crespi, V. H.; Chopra, N. G.; Cohen, M. L.; Zettl, A.; Louie, S. G. Phys. ReV. B 1996, 54, 5927-5931. (27) Banhart, F. Rep. Prog. Phys. 1999, 62, 1181-1221. (28) SimulaTEM; Beltran del Rio, L.; 1.1 ed.; UNAM: Mexico, 1998. (29) Peng, L. M.; Zhang, Z. L.; Xue, Z. Q.; Wu, Q. D.; Gu, N.; Pettifor, D. G. Phys. ReV. Lett. 2000, 85, 3249-3252. (30) Crespi, V. H.; Cohen, M. L.; Rubio, A. Phys. ReV. Lett. 1997, 79, 2093-2096.
Nano Lett., Vol. 3, No. 6, 2003
(31) Ohnishi H.; Kondo Y.; Takayanagi K. Nature 1998, 395, 780-783. Rodrigues, V.; Bettini, J.; Rocha, A. R.; Rego, L. G. C.; Ugarte, D. Phys. ReV. B 2002, 65, 153402-1-4. (32) von Helden, G.; Kemper, P. R.; Gotts, N. G.; Bowers, M. T. Science 1993, 259, 1300-1302. (33) Hunter, J.; Fye, J.; Jarrold, M. F. Science 1993, 260, 784-786. (34) Rinzler, A. G.; Hafner, J. H.; Nikolaev, P.; Lou, L.; Kim, S. G.; Tomanek, D.; Nordlander, P.; Colbert, D. T.; Smalley, R. E. Science 1995, 269, 1550-1553. (35) Xu, C. H.; Wang, C. Z.; Chan, C. T.; Ho, K. M. J. Phys.: Condens. Matter 1992, 4, 6047-6054. (36) Raghavachari, K.; Binkley, J. S. J.Chem. Phys. 1987, 87, 21912197. (37) Lulli, G.; Parisini, A.; Mattei, G. Ultramicroscopy 1995, 60, 187194. Zwanger, M. S.; Banhart, F.; Seeger, A. J. Cryst. Growth 1996, 163, 445-454. (38) Bianchetti, M.; Buonsante, P. F.; Ginelli, F.; Roman, H. E.; Broglia, R. A.; Alasia, F. Phys. Rep. 2002, 357, 459-513. (39) Van Orden, A.; Saykally, R. J. Chem. ReV. 1998, 98, 2313-2357.
NL0341640
755
